Getting more out of a Job plot: determination of reactant to product stoichiometry in cases of displacement reactions and n:n complex formation.

The method of continuous variation (often referred to as Job's method) is an easy and common method for the determination of the reactant stoichiometry of chemical equilibria. The traditional interpretation of Job plots has been limited to complex association equilibria of the type nA + mB ⇌ A(n)B(m), while little focus has been placed upon displacement type reactions (e.g., A + B ⇌ C + D), which can give Job plots that look quite similar. We developed a novel method that allows the user to accurately distinguish between 1:1 complex association, 2:2 complex association, and displacement reactions using nothing more than a pocket calculator. This method involves preparing a Job plot of the system under investigation (using regularly spaced mole fractions), normalizing the measured quantities (such as the concentration of A(n)B(m) or C for the above reactions) to their maximum value (i.e., at mole fraction 0.5), and determining the sum of the normalized values. This sum is then compared with theoretically predicted normalized sum values that depend on the nature of the equilibrium. The relationship between, on the one hand, the sum of the normalized values and, on the other hand, the reaction equilibrium constant and the concentration of the stock solutions used for the preparation of the Job plot is also explored. The use of this new technique for the interpretation of Job plots permits users to readily determine information that can be obtained otherwise only with laborious additional experiments, as illustrated by the analysis of four Job plots taken from the literature.